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How many different committees can be formed from a group of two women

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Joined: 02 Sep 2009
Posts: 50058
How many different committees can be formed from a group of two women  [#permalink]

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New post 10 Jun 2016, 01:01
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:17) correct 37% (01:46) wrong based on 101 sessions

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How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman?

A. 6
B. 8
C. 10
D. 12
E. 16

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Re: How many different committees can be formed from a group of two women  [#permalink]

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New post 10 Jun 2016, 01:14
1
2C1*4C2 + 2C2*4C1 = 16 E is the answer.
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Re: How many different committees can be formed from a group of two women  [#permalink]

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New post 10 Jun 2016, 02:10
2
Bunuel wrote:
How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman?

A. 6
B. 8
C. 10
D. 12
E. 16


2 Women and 4 Men. Three people needed
It is always better to subtract the total from none in case of at least one problems.

Total ways = 6C3 = 20
Total ways without any women = 4C3 = 4

Hence ways in which at least one women will be present = 20 - 4 = 16

Correct option: E
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Re: How many different committees can be formed from a group of two women  [#permalink]

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New post 10 Jun 2016, 09:27
E-16

2C1*4C2 + 2C2* 4C1 =12+4 =16

very easy method
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Re: How many different committees can be formed from a group of two women  [#permalink]

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New post 10 Jun 2016, 09:38
We have 2 women = 2 W, and 4 men = 4M

We want to select 3 people from these 2W and 4M, with at least 1 W

So we can have : WMM or WWM, but no more women since there are only 2.

WMM = 1 from 2 * 2 from 4 = 12
WWM = 2 from 2 * 1 from 4 = 4

So, 12 + 4 = 16
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Re: How many different committees can be formed from a group of two women  [#permalink]

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New post 29 Mar 2018, 03:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many different committees can be formed from a group of two women &nbs [#permalink] 29 Mar 2018, 03:09
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